Thermostatically controlled loads (TCLs) are considered as one of the main demand-side management resources. Although the power rating of an individual TCL is only 2-6 kW, there are millions of TCLs in residential and commercial sectors, making them an important type of distributed energy resources for providing energy and ancillary services. For instance, about 20% of electricity in the U.S. is consumed by the TCLs. See U.S. Energy Information Administration, annual energy review and Buildings energy data book. By varying the length of the cycling intervals of a TCL while keeping temperature variation within its upper and lower temperature limits, the power consumption of the TCL can be modified with little impact on customers' convenience or comfort. Therefore, in recent years, a massive amount of research has been conducted on the development of control and scheduling strategies of TCLs for providing a wide range of grid services. Examples of such services include peak load shaving and load shifting, renewable generation smoothing, load following and regulation services, intra-hour energy market arbitration, contingency type reserve, etc. See J. H. Yoon, R. Baldick, and A. Novoselac, “Dynamic demand response controller based on real-time retail price for residential buildings,” IEEE Trans. Smart Grid, vol. 5, no. 1, pp. 121-129, January 2014; C. Perfumo, J. H. Braslavsky, and J. K. Ward, “Model-based estimation of energy savings in load control events for thermostatically controlled loads,” IEEE Trans. Smart Grid, vol. 5, no. 3, pp. 1410-1420, May 2014; L. C. Totu, J. Leth, and R. Wisniewski, “Control for large scale demand response of thermostatic loads,” in Proc. IEEE Amer. Control Conf., June 2013, pp. 5023-5028; S. A. Pourmousavi, S. N. Patrick, and M. H. Nehrir, “Real-Time demand response through aggregate electric water heaters for load shifting and balancing wind generation,” IEEE Trans. Smart Grid, vol. 5, no. 2, pp. 769-778, March 2014; D. S. Callaway, “Tapping the energy storage potential in electric loads to deliver load following and regulation, with application to wind energy,” Energy Convers. Manage., vol. 50, no. 9, pp. 1389-1400, 2009; O. Mali and P. Havel, “Active demand-side management system to facilitate integration of RES in low voltage distribution networks,” IEEE Trans. Sustain. Energy, vol. 5, no. 2, pp. 673-681, April 2014; J. Mathieu, S. Koch, and D. S. Callaway, “State Estimation and control of electric loads to manage real-time energy imbalance,” IEEE Trans. Power Syst., vol. 28, no. 1, pp. 430-440, February 2013; J. Kondoh, N Lu, and D. J. Hammerstrom, “An evaluation of the water heater load potential for providing regulation service,” IEEE Trans. Power Syst., vol. 26, no. 3, pp. 1309-1316, August 2011; N. Lu, “An of the HVAC load potential for providing load balancing service,” IEEE Trans. Smart Grid, vol. 3, no. 3, pp. 1263-1270, September 2012; M. Vanouni and N. Lu, “Performance indices for evaluating demand response services provided by thermostatically controlled appliances,” in Proc. IEE/PES Transm. Distrib. Conf Expo., April 2014, pp. 1-6; M. Vanouni and N. Lu, “Improving the centralized control of thermostatically controlled appliances by obtaining the right information,” IEEE Trans. Smart Grid, vol. 6, no. 2, pp. 946-948, March 2015; J. L. Mathieu, M. Kamgarpour, J. Lygeros, G. Anderson, and D. S. Callaway, “Arbitraging intraday wholesales energy market prices with aggregations of thermostatic loads,” IEEE Trans. Power Syst., vol. 30, no. 2, pp. 763-772, March 2015; and A. Abiri-Jahromi and F. Bouffard, “Contingency-type reserve leveraged through aggregated thermostatically-controlled loads-Part I: characterization and control,” IEEE Trans. Power Syst., vol. pp. 2015, each incorporated herein by reference in their entirety.
The increasing interest in using TCLs for providing grid services has heightened the need, as recognized by the present inventors, for designing reward systems that motivate the TCLs to perform at their highest level. Although considerable research has been devoted for developing different control and scheduling methods, rather less attentions has been paid to design rewarding mechanisms to compensate individual demand response resources (TCLs). Specifically, this lack of attention is observed for the demand response programs wherein TCLs are recruited to provide intra-hour ancillary services like regulation services.
The foregoing “Background” description is for the purpose of generally presenting the context of the disclosure. Work of the inventor, to the extent it is described in this background section, as well as aspects of the description which may not otherwise qualify as prior art at the time of filing, are neither expressly or impliedly admitted as prior art against the present invention.